How would I set up a smooth rotation for a angled object?
Setting up properly oriented origins for orientated objects with rotation applied.

After the orientation is lost, if there is the possibility of planar faces, it can easily be recreated.


Create a face, which is perpedicular to your desired orientation axis. &#8633; Tab > &#9095; Alt RMB > F
Since my faces median is even at the desired center, I snap the cursor to selected. &#8679; ShiftS > Cursor To Selected





Add a helper object, in my case a cube. &#8679; ShiftA > Cube





Apply all transformations of the helper cube.
Activate snapping and set it to Closest Face.


Snap ON
Faces
Closest
Align rotation ON
Project individual[ly] ON






Grab the cube G and by moving it onto the helper face, it will align itself.
Snap it to the cursor afterwards. &#8679; ShiftS > Selection to Cursor





Select the original object  RMB, then &#8679; Shift RMB select the helper object, and join them &#9096; CtrlJ. The will merge into one object which still holds the helper objects orientation.
Delete the unnecessary faces and vertices.